DOC PREVIEW
UT Knoxville STAT 201 - 2) cor_reg_mutliple_IVs

This preview shows page 1-2-19-20 out of 20 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 20 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 20 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 20 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 20 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 20 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

SAS Output for Simultaneous Multiple RegressionANOVA Tables For Full and Restricted ModelsSAS Code for Standardizing Variables and Obtaining a Standardized Regression EquationSAS Output for Multiple Regression Conducted on Standardized VariablesHierarchical Regression in SASRelevant Output For Hierarchical Analysis in SASRelevant Output For Hierarchical Analysis in SPSSMULTIPLE REGRESSIONEstimating the Partial Regression Parameters of a Multiple Regression in SASCharacteristics of the Overall ModelCharacteristics of the individual Regression ParametersPARTIAL CORRELATION AND SEMI PARTIAL CORRELATIONANALYTIC STRATEGIES OF MRC:SIMULTANEOUS, HIERARCHICAL, AND STEPWISESimultaneous AnalysisHierarchical AnalysisStep-Wise AnalysisCourse: Multiple Regression Topic: Correlation & Regression With Multiple Variables 1 CORRELATION & REGRESSION WITH MULTIPLE VARIABLESWe previously discussed the bivariate case of correlation and regression in which we examined the association between two variables and estimated a model linking one variable to the other. Today we will begin our exploration of multiple correlation and regression (MCR) in which we account for the shared associations among multiple variables. As you will discover, bivariate correlation and regression can provide a deceptive or inaccurate picture of the actual association between two variables. The academic salary data provides a glimpse into the potentially deceptive lens of bivariate associations.The following table contains the bivariate (or zero-order) correlations among all of the variables in the academic-salary data set (these correlations can be obtained in SAS by specifying “proc corr; var salary phd pubs sex citations; run;”). Variable Salary PhD Pubs Sex CitationsSalary - - - - -PhD .62 - - - -Pubs .46 .68 - - -Sex -.26 -.15 .05 - -Citations .51 .46 .30 -.01 -Note. Sex is coded such that 0 = male and 1 = female.If we focus only on the correlations in the “Salary” column, we might conclude that salary increases with increases in years since earning a PhD, number of publications, and numberof citations and that females have lower salary’s than males. However, an examination of the remaining columns might raise suspicion in our initial conclusion. Notice, for example, that years since earning a PhD and publications share a modest bivariate association. Consequently, some of the association between years since PhD and Salary might actually be attributable to number of publications. Likewise, notice that publications and citations are also correlated. Consequently, some of the correlation between salary and publications may contain information about the association between salary and citations. Furthermore, there maybe some unmeasured variable that is related to salary and the other variables and the association among salary and the other variables might really be attributed to the unmeasured variable. This example demonstrates that bivariate correlations do not always reveal the true association between variables because the bivariate correlation does not remove the influence of other variables. To accurately assess the association between X and Y we need to remove from the bivariate association the influence of all other variables that are associated with both X and Y.Obviously this is a formidable task and is precisely what MRC helps us accomplish. Keep in mind, however, that MRC can suffer the same weakness of bivariate correlation and regression. When important variables are excluded from a MRC analysis the associations revealed by the MRC analysis have not been “purified” of the shared associations with the excluded variables. The only pure panacea to the problems of correlated variables and unmeasured influences is gathering data with the experimental method. Unfortunately, many issues of study are not amenable to an experimental design (e.g., we can’t randomly assign persons to be male or female). What follows are the basics of MRC.Course: Multiple Regression Topic: Correlation & Regression With Multiple Variables 2 MULTIPLE REGRESSIONMultiple regression provides a linear model of the association between a dependent (or criterion) variable and multiple independent (or predictor) variables. The advantage of multiple regression is that it unconfounds the effect of each predictor variable on the dependent variable from the effect of the other predictor variables in the model. The basic notation for a linear model is:21212112ˆXBXBAYYYY The betas (B’s) in multiple regression are partial betas and reflect the effect of each variable on Ycontrolling for the effect of the other variables. That is, 21YB reflects the effect of X1 on Y controlling for the effect of X2. Likewise, 12YB reflects the effect of X2 on Y controlling for the effect of X1. The betas are referred to as partial betas because each beta has partialled from it the correlated effects of other variables in the model. The Y-intercept (12YA) indicates the predictedvalue of Y when all of the X’s are equal to zero (i.e., the value of Y at which the regression line crosses the Y-axis). Keeping in mind that the betas are partial regression coefficients we can simplify the notation of the model as follows: 2211ˆXBXBAY We’ll use the salary example to demonstrate the difference between bivariate and multiple regression. The following bivariate regression models reflect the bivariate association between salary and publications and citations, respectively.Salary = 21106 + 566PubsSalary =22976 + 1918CitationsThe first model indicates that salary increases $566 with each publication. The second model indicates that salary increases $1,918 each time a publication is cited. Given that publications and citations are correlated (r=.30, see table of bivariate correlations), the beta linking salary to publications may convey some of the effect of citations on salary (and vice-versa for the beta linking salary to citations). Multiple regression, however, will remove the overlapping information from each beta and reveal the effect of publications on salary that is independent of citations and the effect of citations on salary that is independent of publications. For example, themultiple regression model in which salary is simultaneously regressed on publications and citations is:Salary = 20285 + 418Pubs +1536CitationsNotice that the partial betas for publications and citations are smaller


View Full Document

UT Knoxville STAT 201 - 2) cor_reg_mutliple_IVs

Documents in this Course
Chapter 8

Chapter 8

43 pages

Chapter 7

Chapter 7

30 pages

Chapter 6

Chapter 6

43 pages

Chapter 5

Chapter 5

23 pages

Chapter 3

Chapter 3

34 pages

Chapter 2

Chapter 2

18 pages

Chapter 1

Chapter 1

11 pages

Load more
Download 2) cor_reg_mutliple_IVs
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view 2) cor_reg_mutliple_IVs and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view 2) cor_reg_mutliple_IVs 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?